When the idea of a television adaptation of Margaret Atwood’s feminist classic, The Handmaid’s Tale, was mooted, the key phrase attached was “with Elisabeth Moss playing the lead”. The 34-year-old’s involvement was a small but clear signal of reassurance to fans of the source material: this was an adaptation to trust.

Next Sunday, British fans will get a chance to judge whether their faith was well placed as The Handmaid’s Tale arrives on Channel 4. In the US, the series has been rapturously received, hailed by the New York Times as “unflinching, vital and scary as hell”.

The biggest plaudits, however, were saved for Moss, who plays Offred, the title’s handmaid and a woman reduced by a repressive and patriarchal society into sexual enslavement, her old name removed, her new one the signifier of her owner, making her literally Of-Fred. The Boston Globe was impressed: “With The Handmaid’s Tale, Moss establishes herself as one of TV’s best dramatic actresses.”

In truth, she’d done that already. Twice. As Peggy Olson, the dowdy Catholic secretary turned go-getting copy chief on Mad Men, Moss became the no-nonsense heroine for a generation of cable TV watchers. Then, with Mad Men coming to an end, Moss ensured she would not be consumed by the role that defined her.

Going to New Zealand, she took the lead in Jane Campion’s bleak, bruising Top of the Lake, a dark, dense story about a violent, closed-off community, which returns for a second series this summer. Moss will again play troubled detective Robin Griffith, with Campion full of praise for her star: “She does a very Elisabeth Moss thing, which is… show strength and vulnerability at once, and also mystery.” Mad Men creator Matthew Weiner was more succinct, stating in a Guardian profile that the only two things you need to know about Moss were that she “never gives a bad take and is a rubbish drinker”. Small wonder New York magazine recently named her “the Queen of Peak TV”.

The down-to-earth and outwardly easy-going Moss prefers to play down the praise. “I wish I was super-serious, anguished. I see those actors and I am like, oh God, they are so cool and they seem so interesting,” she said. “I don’t take acting that seriously. I love my work but I do not think that I am saving the world... I am a Valley Girl.”

She wasn’t entirely joking, although beneath the sunny exterior lurks a more complicated soul. She was born in Los Angeles, California, in 1982 and grew up in Laurel Canyon. Her British father, Ron, was a jazz musician and music manager, her American mother, Linda, a harmonica player in blues bands. She and her younger brother, Derek, were raised in a relaxed environment where the arts had more value than a traditional education.

“My earliest memories are at the Blue Note in New York or backstage at different theatres or different clubs,” she told the Guardian. “We grew up with musicians coming over jamming. We had tons of instruments. So holidays were always like, 50 people would come over and there would be a jam session with everyone playing jazz. When I was 12 I didn’t know about Nirvana or Oasis or any of those people. I was listening to Ella Fitzgerald and Gershwin.”

There was, however, a strange wrinkle in this idyllic picture of bohemian freedom – the family were Scientologists and Moss, raised in the church, remains in it today. “I feel it has given me a sanity and a stability that I’m not sure I would necessarily have had,” she told the Times in 2010. In recent years, perhaps mindful of reputation (hers and the church’s), she has become more reticent about her religion: “I said what it meant to me and anyone can go and look at that if they want to know what I feel. But now it’s private, off limits.”

If Scientology and music were two crucial poles of her upbringing, the third, and in some ways most important, was ballet. As a child, she pursued dual careers, taking roles in commercials and made-for-TV movies while training as a dancer. At 15, she chose acting, noting it was the easier option. It was certainly the right one. By 17, she was playing the daughter of the president (Martin Sheen) in The West Wing; by 19, she had moved to New York to star in a play; at 23, having already been acting professionally for more than a decade, she was cast as Peggy in Mad Men.

“In my mind, there was something far more difficult than acting, which was either ballet or music,” she told the Independent in an attempt to explain why her work came so naturally to her. “You have to practise for hours every day. And that’s how you make it. That kind of discipline was very grounding.”

She is an actress of great control who can say a lot while seeming to do very little and whose performances Campion describes as “coming from the inside out”. Yet alongside this restraint comes a natural warmth, which makes even the most closed-off character appear sympathetic. It’s a skill that has stood her in particularly good stead on The Handmaid’s Tale, where Offred hides her resistance to the new regime behind the blank face she presents to the world. She can snap quickly out of a role once off stage and in the wings. “I barely hang on to it while we’re filming,” she admitted to New York magazine. “I am totally that person that they yell ‘cut’ and I’m making jokes and doing stupid stuff. It’s fake to me to be any other way.”

Away from the camera, she is relaxed and a little goofy with a reputation as a joker. “She’s not one of those actresses who is walking around with her headphones on listing to Nine Inch Nails to get into a scene,” Mark Duplass, who worked with her on The One I Love, told New York magazine. “She’s joking around causally and then you yell ‘action’ and her heartbeat goes up to 150 beats per minute.”

Having spent most of her life working, she admits to being occasionally emotionally naive; in an otherwise lighthearted Q&A, she stated that her biggest secret was “I tend to fall in love a little bit too easily sometimes”. A short, unhappy marriage to comedian Fred Armisen, which lasted less than a year amid reports that Armisen thought he was marrying Peggy Olson, not Elizabeth Moss, seems to highlight that truth. “Looking back, I feel like I was really young,” she told New York magazine. “It was extremely traumatic and awful and horrible. At the same time, it turned out for the best. I’m glad I’m not there. I’m glad it didn’t happen when I was 50. Like, that’s probably not going to happen again.”

Perhaps because of this she now prefers a quiet life, renting apartments in New York’s Upper West Side and West Hollywood, LA, and hanging out at a handful of familiar haunts. She says she prefers staying in watching TV to going out but is also a committed shopper. “Whenever she likes something, be it food or clothes or shoes, she orders heaps of it,” noted Campion. “I remember her apartment in New Zealand was piled with boxes. She does girly-girl very well.”

A self-described “card-carrying feminist”, Moss ran in trouble last month after appearing to suggest that The Handmaid’s Tale was a story about “human” rather than “women’s rights”. Always sensitive to perceptions, she was quick to clarify, stressing that she had merely wanted to highlight “the different problems we are facing – the infringements on a lot of different human rights OBVIOUSLY, all caps, it’s a feminist story”.

It was a rare misstep from a preternaturally poised actress and unlikely to be repeated in the near future.

THE MOSS FILES

Born Elisabeth Singleton Moss in Los Angeles, California, 24 July 1982. Her parents were both musicians and she was raised a Scientologist.

Best of times

As Mad Men’s Peggy Olson, she was nominated six times for a best actress Emmy. She has yet to win.

Worst of times

A whirlwind romance with Fred Armisen resulted in a marriage that collapsed in under a year.

What she says

“When someone puts up the gif of Peggy walking down the hall with the box and the cigarette and connects it to International Women’s Day or the Hillary Clinton campaign, I’m always like, ‘Damn, that’s so cool’.”

What they say

“She’s a little bit like a Mona Lisa. There’s a lot that she’s not showing you.”